text: Water is approximately 800 times more dense than air. However, air is approximately 15,000 times more compressible than water. The velocity of sound, υ, in a homogeneous liquid or gas is given by the following equation:
  where ρ is the mass density and K the compressibility of the gas or liquid. K is given as:
  where V is the volume of the medium, and dV is the volume decrease due to the pressure increase dp of the sound wave. When water is filled with air bubbles, the fluid density is essentially the density of water, and the air will contribute significantly to the compressibility. Crawford derived the relationship between fractional bubble volume and sound velocity in water, and hence the sound frequency in water, given as.
  where υ and υ are the velocities of sound in pure and bubble-filled water, respectively, f and f are the frequencies of sound in pure and bubble-filled water, respectively, V is defined as the fractional volume occupied by gas bubbles, and α is a constant. When the solvent is water and the gas is air, the value of α is 1.49 × 10.
  The effect of changes in solution density and solution compressibility are additive and reinforce the phenomenon, causing a significant decrease in the velocity of sound and, therefore, a significant decrease in the frequency of sound passing through an aerated solution.